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Title: Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers

Abstract

The wave equation in a thin laminated beam with contrasting stiffness and density of layers is considered. The problem contains two parameters: ε is a geometric small parameter (the ratio of the diameter and its characteristic longitudinal size) and ω is a physical large parameter (the ratio of stiffness and densities of alternating layers). The asymptotic behavior of the solution depends on the combination of parameters ε{sup 2}ω. If this value is small, then the limit model is the standard homogenized one-dimensional wave equation. On the contrary, if ε{sup 2}ω is not small, then the limit model is presented by the so-called multicontinuum model, i.e., multiple one-dimensional wave equations, coupled or noncoupled and “co-existing” at every point. The proof of these results uses the milticomponent homogenization method.

Authors:
 [1]
  1. University of Lyon Institute Camille Jordan UMR CNRS 5208 and SFR MODMAD FED 4169 (France)
Publication Date:
OSTI Identifier:
22773946
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 232; Journal Issue: 4; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; DENSITY; FLEXIBILITY; GEOMETRY; HOMOGENIZATION METHODS; LAYERS; ONE-DIMENSIONAL CALCULATIONS; SUPPORTS; WAVE EQUATIONS; WAVE PROPAGATION

Citation Formats

Panasenko, G. P., E-mail: Grigory.Panasenko@univ-st-etienne.fr. Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3889-7.
Panasenko, G. P., E-mail: Grigory.Panasenko@univ-st-etienne.fr. Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers. United States. doi:10.1007/S10958-018-3889-7.
Panasenko, G. P., E-mail: Grigory.Panasenko@univ-st-etienne.fr. Sun . "Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers". United States. doi:10.1007/S10958-018-3889-7.
@article{osti_22773946,
title = {Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers},
author = {Panasenko, G. P., E-mail: Grigory.Panasenko@univ-st-etienne.fr},
abstractNote = {The wave equation in a thin laminated beam with contrasting stiffness and density of layers is considered. The problem contains two parameters: ε is a geometric small parameter (the ratio of the diameter and its characteristic longitudinal size) and ω is a physical large parameter (the ratio of stiffness and densities of alternating layers). The asymptotic behavior of the solution depends on the combination of parameters ε{sup 2}ω. If this value is small, then the limit model is the standard homogenized one-dimensional wave equation. On the contrary, if ε{sup 2}ω is not small, then the limit model is presented by the so-called multicontinuum model, i.e., multiple one-dimensional wave equations, coupled or noncoupled and “co-existing” at every point. The proof of these results uses the milticomponent homogenization method.},
doi = {10.1007/S10958-018-3889-7},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 4,
volume = 232,
place = {United States},
year = {2018},
month = {7}
}